Action Does NOT Equal Reaction ?

  • Thread starter STAii
  • Start date
  • Tags
    Reaction
In summary, the author discusses the weak and strong forms of Newton's third law and how they differ. Goldstein states that the weak form does not always hold, and classical mechanics must use the strong form. Pete quotes from a textbook that says that a particle with an electric field has a magnetic field. Arcnets says that the fields generated by charges are not always equal and opposite. French discusses how relativistic mechanics does not always follow the principle of action and reaction.
Physics news on Phys.org
  • #2
Originally posted by STAii
Is it true ?
No. They assume that the electric field propagates instantaneously, while the magnetic field does not. Which is false .
 
  • #3
a little bit off topic

The 2 particles are negatively charged, not positively charged, right?
 
  • #4
Originally posted by STAii
From this link http://jnaudin.free.fr/lifters/lorentz/index.htm
Is it true ?

There are two forms of Newton's third law
(1) Weak form - forces are equal and opposite but not along a line
(2) Strong form - forces are equal and opposite and along a line

The weak form does not hold for all types of forces.

It'll be simpler if I just quote "Classical Mechanics - Third Edition," Goldstein, Safko and Poole. Page 7-8

In a system involving moving charges, the forces between charges predicted by the Biot-Savart law may indeed violate both forms of the action and reaction law.*

*(footnote) If two charges are moving uniformly with parallel velocity vectors that are not perpendicular to the line joining the charges, then the net mutual forces are equal and opposite but do not lie along the vector between the charges. Consider, further, two charges moving (instantaneously) so as to "cross the T." i.e. one charge moving directly at the other, which in turn is moving at right angles to the first. Then the second charge exerts a nonvanishing magnetic force on the first, without experiencing any magnetic reaction force at that instant.

Pete
 
  • #5


Originally posted by pmb
the forces between charges predicted by the Biot-Savart law ...
Biot-Savart is for stationary currents - not single moving particles. Because there's nothing 'stationary' when you have a single moving particle. There's no such thing as a 'magnetic field of a single moving particle'. Each particle is affected only by the Lorentz-transformed Coulomb field of the other one, and since Lorentz-transformation is symmetrical, so is the interaction. Don't be fooled...
 
  • #6


Originally posted by arcnets
Biot-Savart is for stationary currents - not single moving particles.


I assume you understood what Goldstein meant. Is that correct? Do you disagree with his conclusion?

There's no such thing as a 'magnetic field of a single moving particle'.

Sure there is. Its a fact of relativity. If a particle has a pure electric field in its rest frame then there will be a magnetic field in a frame in which the particle is moving - that's a basic fact of relativistic electrodynamics. Just look at the the relations for how the fields transform. You'll see that this is so.

Each particle is affected only by the Lorentz-transformed Coulomb field of the other one, and since Lorentz-transformation is symmetrical, so is the interaction. Don't be fooled...

That is incorrect. E.g. In frame S there is a moving particle with a charge. In S there is both an electric and a magnetic field due to that charge. If there is another charge moving in S then the force on that charge will be F = q[E + vxB] where E and B are generated by the first charge.

If E is the electric field of the moving charge and v is the velocity of the moving charge then the magnetic field of the moving charge is given by

B = vxE

For a derivation see Feynman Lecturers Vol II page 26-3. For a picture of the magnetic field see Figure 26-5 in V-II.

There should be something about this in the Feynman Lectures. Do you have them?

The nature of relativity prevents an action reaction forces between particles in general - what is equal and opposite in one frame is, in general, not equal and opposite in another.

French discusses this too. He makes a very important point. From "Special Relativity," A.P. French, page 224

It is worth pointing out that one of Newton's basic assertions about forces between bodies - the equality of action and reaction - has almost no place in relativistic mechanics. It must essentially be a statement about about force acting on two bodies, as a result of the mutual interaction, *at a given instant.* And, because of the relativity of simultaneity, this phrase has no unique meaning unless the points at which the forces are applied are separated by a neglegible distance. [...] What the relativistic analysis does do, however, is to compel us to conclude that, according to measurements in a given inertial frame, the forces of action and reaction are in general *not* equal and opposite, and so the total momentum of the interacting particles is no conserved instant by instant.
The missing momentum is, of course, in the field. I.e. the EM field has momentum so that the total momentum of Fields + Particles is constant.

Pete
 
  • #7
pmb,
I admit I didn't put enough thought into this. I'll check - just don't have the time now, hang on please.
 
  • #8
Originally posted by arcnets
pmb,
I admit I didn't put enough thought into this. I'll check - just don't have the time now, hang on please.

So'kay! Take your time. That's why we're all here! :-)

Pete
 
  • #9
pmb,
well I gave it some thought. Here's my (unsatisfactory) results:

1) There is indeed such a thing as a magnetic field of a single moving particle. The classical approximation is:
B = q/c * vxr/r3.
And that was indeed named after Biot/Savart. So you are right, and I was wrong.

2) Let's now treat the problem completely classical. Let particle 2 be in the path of particle 1, and moving at right angles. Let for simplicity q = c = r = 1. Then, we get indeed
F1 = r - v1v2,
F2 = -r.
In other words, actio=reactio is indeed violated.

3) Indeed, the missing momentum must go into the field (see e.g. Jackson, chapter 6.8.).

4) Here my trouble begins. How can any momentum go into the field in such a simple configuration? The only answer I can think of is: Bremsstrahlung. But I don't see how this classical treatment of the problem can produce any e.m. radiation (i.e. sinusoid waves)...!?

5) My next thought was, we should treat this with full SR. In Jackson, chapter 11.10, I found the following:
If two particles move at relative speed v, then the field of one particle seen in the rest frame of the other is:
Elongitudinal = [gamma]qvt/(b2+[gamma]2 v2 t2)3/2
Etransversal = [gamma]qb/(b2+[gamma]2 v2 t2)3/2
B = [beta] Etransversal.
Where b is the shortest connection of both paths, t=0 when they are closest, and B is, of course, at right angles with v and b.

Now, since b is invariant (because it's at right angles with both paths), this result is indeed symmetric, since all you do is replace v by -v and b by -b when switching from one particle to the other.

Now this is strange, because in a particle's rest-frame it should not feel any Lorentz force at all, no matter what B is. Plus, I don't know at all how to translate this into forces in the lab (or any other) frame. I still suspect, when doing this properly, actio=reactio will hold. That is, there will be at least one frame of reference in which it will hold. Maybe the center-off-mass one.

Any help?


Edit: corrected 1 error, and made some formulae better legible. Couldn't make the gamma small, however. It should be...
 
Last edited:
  • #10


Thanks for the quotes, Pete. I could have used them last year when on another forum I received a lot of flak for stating that... to adopt relativity one has to be willing to give up the concept of Newton's 3rd law.

J.L. Naquin's site (given in the 1st post) has an excellent graphic which illustrates precisely the point made in your referenece in Goldstein's footnote, which show how when two charges approach each other with orthagonal trajectries, one avoids the magnetic reaction force - at least temporarily.

Which brings us to the next point, which he only briefly mentioned, and you brought up succintly.

Originally posted by pmb

The missing momentum is, of course, in the field. I.e. the EM field has momentum so that the total momentum of Fields + Particles is constant.

[/B]

So you therefore would say that the 'missing' momentum remains in the field? Or would you say the field produces a back reaction on the source particle - thus no real asymmetry?

Creator
 
Last edited:
  • #11


Originally posted by Creator
Thanks for the quotes, Pete. I could have used them last year when on another forum I received a lot of flak for stating that... to adopt relativity one has to be willing to give up the concept of Newton's 3rd law.

J.L. Naquin's site (given in the 1st post) has an excellent graphic which illustrates precisely the point made in your referenece in Goldstein's footnote, which show how when two charges approach each other with orthagonal trajectries, one avoids the magnetic reaction force - at least temporarily.

Which brings us to the next point, which he only briefly mentioned, and you brought up succintly.



So you therefore would say that the 'missing' momentum remains in the field? Or would you say the field produces a back reaction on the source particle - thus no real asymmetry?

Creator

I hear ya! People hate it when you disagree with them and will refuse to give up their old ideas. A person that used to post here is flaming me elsewhere. It's a result of his misunderstanding of Einstein's "photon in a box" gerdanken experiment. He shakes at the notion that light has mass! But alas - it's true!

Just made a new web page on the center of mass for a relativistic system

See -- http://www.geocities.com/physics_world/sr/center_of_mass.htm

That's in preperation for a new web page on Einstein's "photon in a box" thing. I've defined and described it here

www.psyclops.com/hawking/forum/printmsg.cgi?period=current&msg=59744

Pete
 
  • #12
There's a problem with equation 1 on your page. mk is not a constant with respect to t; as time changes, particke k's velocity may change, which will thus change particle k's relativistic mass. Thus, you cannot, in general, perform the last step in equation 1.

In particular, this means that there's no reason that the center of mass, as you've defined it, should have a constant velocity (even in the presense of no external forces).
 
  • #13
Originally posted by Hurkyl
There's a problem with equation 1 on your page. mk is not a constant with respect to t; as time changes, particke k's velocity may change, which will thus change particle k's relativistic mass. Thus, you cannot, in general, perform the last step in equation 1.


Please take close note of the very first sentence, i.e.

"Consider a system of particles, all of which move at constant velocity..."

Pete
 
  • #14
lol I read the whole thing twice, and never noticed the text up there before the diagram!
 
  • #15
Originally posted by Hurkyl
lol I read the whole thing twice, and never noticed the text up there before the diagram!

I have it when that happens! :-D

I've just been going over Einstein's 1906 "photon in a box" paper over the last week. This seems quite compatible with his comments and derivations and conclusions.


I've just modified that comment. Looking over it I now see that all I needed to do was require that that the speed remain unchanged - not the velocity. So now the particles can move in a cirlce!

Pete
 
  • #16


Originally posted by pmb
People hate it when you disagree with them and will refuse to give up their old ideas. He shakes at the notion that light has mass

Yes yes, photons have non-vanishing relativistic mass but vanishing rest mass.

The idea you seem to "hate" giving up is that it's wrong to view massless particles as pure energy.

I'm pretty sure that Rindler would tell you that you're twisting his view about the efficacy of using the term "relativistic mass" into something he never intended or agrees with.
 
  • #17


Originally posted by jeff
The idea you seem to "hate" giving up is that it's wrong to view massless particles as pure energy.
In the first I've never considered a photon as something being "pure energy." The notion of anything being pure energy makes no sense to me.

In the second place if you're referring to the notion of a photon having mass = energy/c^2 then you're very much wrong. It's not something I've be reluctant to give up. It's been something I've come to accept - that's quite a big difference. When I first heard of this notion (about 8 years ago as I recall) I assumed people were just misinterpreting Einstein. As I studied Einstein's original work and all the many artilces on it that followed over the years since 1905 I've come to accept that a mass of a photon of m = E/c^2 is exactly what Einstein had in mind and that it makes perfect sense. And this is something which can be found in many relativity texts.

For example: from "Relativity: Special, General and Cosmological," Rindler, Oxford Univ., Press, (2001), page 120

According to Einstein, a photon of frequency v has energy hv, and thus (as he came to realize several years later) a finite mass hv/c^2 and a finite momentum hv/c.

re -

I'm pretty sure that Rindler would tell you that you're twisting his view about the efficacy of using the term "relativistic mass" into something he never intended or agrees with.

Why would you think that? IMHO - The notion of relativistic mass is the closest thing there is to what would consider as being mass. And that definition of "mass," when defined rigorously, demands that light has mass. A box containing a gas of photons of total energy U has inertial properties of that of a mass of energy m = U/c^2. So the inertial mass the box, whose mass is M, is that of an object whose mass is (M+m). According to the equivalence principle itg can be shown that the photon gas has a passive gravitational mass. A beam of light generates a graviational field and therefore has an active gravitational mass.


This notion of an EM field having mass was the view Einstein arrived at in 1906 in what has come to be known as Einstein's photon in a box thought experiment. The paper concluided with Einstein deducing that u = "energy density of EM field" has a mass density of u/c^2.

In any case I know relativity so I can form my own opinions. I just happen to agree with Rindler and everyone on this point. I gave you another example if you recall

http://www.geocities.com/physics_world/Guth.jpg

I'm pretty sure that Rindler would tell you that you're twisting his view about the efficacy of using the term "relativistic mass" into something he never intended or agrees with.

What are you basing this opinion of that Rindler thinks on?

Pmb
 
  • #18
Incidentally, just because the sum of the momenta of two or more photons may have mass does not mean each individual photon has mass.
 
  • #19
Originally posted by Hurkyl
Incidentally, just because the sum of the momenta of two or more photons may have mass does not mean each individual photon has mass.

For a system of two photons moving in opposite directions there is a zero momentum frame. Therefore even though both photons have zero proper mass the system has a non-zero proper mass. In fact I was just explaining this last night to someone. I.e. I was discussing black body radiation - such raidation has an energy-momentum tensor of a perfect fluid.


Did you get the impression that I thought any different? If so then you were mistaken.


Pmb
 
  • #20
In fact the energy of just one photon, if high enough, can be used to create a new particle and antiparticle. The photon ceases to exist in this pair production
 
  • #21
Originally posted by selfAdjoint
In fact the energy of just one photon, if high enough, can be used to create a new particle and antiparticle. The photon ceases to exist in this pair production

Yes. Quite true. And of course there must be another particle around to facilitate the pair production. Otherwise there would be a violation of the conservation of momentum.

Pete
 
  • #22
From the article:
Note : To be in agreement with Newton's 3rd law, it would be necessary to take into account the moments of the magnetic and electric fields.
Am I misunderstanding or does that sentence translate into: 'if we ignore some of the forces, the forces are imbalanced'?
 
  • #23
Originally posted by russ_watters
From the article: Am I misunderstanding or does that sentence translate into: 'if we ignore some of the forces, the forces are imbalanced'?

Was that something I wrote?

Pete
 

1. What is the scientific principle of "Action does not equal reaction"?

The scientific principle of "Action does not equal reaction" is a concept in physics known as the principle of non-reciprocity, which states that the forces acting on two objects do not necessarily have equal magnitudes and opposite directions. This is in contrast to the commonly known law of motion, "For every action, there is an equal and opposite reaction."

2. How does this principle differ from the law of motion?

This principle differs from the law of motion because it allows for the possibility that the forces acting on two objects may not be equal and opposite. This means that the acceleration of each object may not be the same, and therefore, the resulting motion will not be equivalent.

3. What are some examples of "Action does not equal reaction" in everyday life?

One example of this principle can be seen in the motion of a rocket. The rocket exerts a force on the gas it expels, causing it to accelerate in one direction. However, the gas exerts a smaller force on the rocket in the opposite direction, resulting in the rocket's overall motion. Another example is when a person jumps off a boat. The person exerts a force on the boat, causing it to move in the opposite direction, but the boat's movement is much smaller due to its larger mass.

4. How does this principle impact the design and function of objects and machines?

This principle is essential in the design and function of objects and machines, such as engines and rockets. It allows engineers to create more efficient and effective designs by understanding the unequal and non-reciprocal forces at play. For example, rocket engines are designed with directed nozzles to maximize the force exerted in one direction and minimize the force in the opposite direction.

5. Is the principle of "Action does not equal reaction" always applicable in the physical world?

While this principle applies to many situations in the physical world, there are also instances where the forces acting on two objects may be equal and opposite. The law of motion is still a fundamental principle in physics, and the principle of non-reciprocity is an extension of it. Therefore, both principles are necessary to fully understand and explain the motion of objects in the physical world.

Similar threads

  • Other Physics Topics
Replies
3
Views
9K
  • Other Physics Topics
Replies
7
Views
2K
  • Other Physics Topics
Replies
8
Views
2K
  • Special and General Relativity
Replies
15
Views
970
Replies
4
Views
2K
  • Classical Physics
2
Replies
49
Views
2K
  • Classical Physics
Replies
8
Views
1K
  • High Energy, Nuclear, Particle Physics
Replies
18
Views
326
  • Engineering and Comp Sci Homework Help
Replies
6
Views
659
  • Other Physics Topics
Replies
7
Views
1K
Back
Top